Page:Calculus Made Easy.pdf/113

CHAPTER XI.

MAXIMA AND MINIMA.

One of the principal uses of the process of differentiating is to find out under what conditions the value of the thing differentiated becomes a maximum, or a minimum. This is often exceedingly important in engineering questions, where it is most desirable to know what conditions will make the cost of working a minimum, or will make the efficiency a maximum.

Now, to begin with a concrete case, let us take the equation

$y=x^{2}-4x+7$.

Fig. 26.

By assigning a number of successive values to $x$, and finding the corresponding values of $y$, we can